Fluid-flow machinery blading



H. STARGARDTER FLUID-FLOW MACHINERY BLADING 2 Sheets-Sheet 1` July 17, 1962 Filed May 18, 1960 July 17, 1962 Filed May 18, 1960 STARGARDTER 3,044,746

FLUID-FLOW MACHINERY BLADING F/efpafA/cy 2 Sheets-Sheet 2 IIEII "E EIY Mvg/Mw United States Patent O 3,044,746 FLUID-FLOW MACHINERY BLADING Hans Stargardter, Deer Park, Ohio, assignor to General Electric Company, a corporation of New York Filed May 18, 1960, Ser. No. 29,949 6 Claims. (Cl. 253-77) This invention relates to iluiddiow machinery blading and, more particularly, to uid-fiow machinery blading having improved vibrational stability.

In the continuing search for more practical fluid-flow machinery there has been an increasing trend toward lighter and more exible components, particularly in the design of turbomachinery blading. This has resulted in the general problem of higher stresses and, in many applications, the particular problem of increased susceptability of blades to vibrational instability. This problem has proven especially troublesome in turbomachine comy,pressor design. In particular, problems of vibrational instability have been encountered in the front end of the compressor where relatively long, flexible blades can be heavily loaded. This condition is often accompanied by a particular form of vibrational instability known as flutter. Flutter in a turbomachinery blade is primarily a twisting form of vibration, which can be caused by a smoothly flowing fluid passing over the blade in the abence of any externally applied vibrating impulse. It is known that most types of flutter are dependent on the fundamental naturalfrequency of the blade in torsional vibration, i.e., a mode of vibration wherein the blade twists or oscillates about an axis near the center of the blade which extends generally parallel to the blades longitudinal axis. It is also known that if the fundamental natural torsional frequency of the blade is shifted upwards, blade stability Will be improved, i.e., the blade will be less likely to burst into destructive flutter. This is because, all other ,things being equal, a blade having a relatively high fundamentaltorsional frequency is stiffer, i.e., it offers higher resistance to motion, than a blade having a lower fundamental torsional frequency.

An approximate mathematical indicator of blade stability is the parameter reduced velocity Y bait where v If|=air velocity relative to the blade (ft/sec.)

For optimum stabilization the reduced velocity must not exceed a certain value dependent on the blades application. It is apparent from the above expression that with a given relative air velocity, increasing the torsional frequency or the size of the blade chord will result in a lower value for the parameter. If the blade chord is increased it will be found that the blade almost always becomes too heavy for more advanced types of airborne turbo-machinery, in particular, machinery wherein relatively long, vilexibleblades are utilized. On the other hand, it has hitherto been thought undesirable to lower thevalue of the parameter by retaining the original chord dimension 'and raising the torsional frequency, particularly in the firstfew stages of a compressor. because the known methods of raising torsional frequency have always resulted in a corresponding rise in the fundamental natural frequency of the blade in flexural vibration, Le., the vibrational mode wherein the blade bends at the root. This is undesirable because, in most instances, the fundamental natural flexural frequency of This is ICC the blade must be kept at a predetermined level to avoid known sources of excitation.

Accordingly, an object of the present invention is to provide iluiddiow machinery blading having improved vibrational stability.

A more specific object of the present invention is to provide a fluid-flow machinery blade having a relatively high fundamental torsional frequency without a correspondingly high fundamental flexural frequency, such as is common in known conventional blade design.

Briefly, one embodiment of my invention comprises a fluid-flow machinery blade having an airfoil including root, tip, and intermediate portions and having an improved stiffness distribution wherein the thickness distribution in the blade airfoil, proceeding from the root portion to the tip portion, initially decreases at a decreasing rate and thereafter decreases at an increasing rate to provide the blade with a relatively high fundamental torsional frequency without a correspondingly high fundamental flexural frequency such as would occur in a conventional blade design.

While Ifparticularly point out and distinctly claim my invention at the conclusion of the specification, the invention will perhaps be better understood and other objects and advantages become more apparent by a reading of the following description taken in conjunction with the accompanying drawings wherein:

IFIGS. la and lb are schematic diagrams showing a typical fluid-how machinery blade considered as an elastic system, the diagrams illustrating flexural and torsional modes of vibration; and

FlG. 2 is a frequency plot of certain parameters inherent in a typical turbomachine compressor which must be considered in the design of the machine; and

FlG. 3 is a graph illustrating the bending moment and the torsional (twisting) moment distributions in a fluidflow machinery blade at resonance; and

FIG. 4 is a perspective view of a typical fluid-flow machinery blade incorporating one means for achieving the improved stiffness distribution of my invention; and

FIG. 5 is a graph comparing the thickness distribution in a typical conventional blade as compared to the distribution in the blade shown in FIG. 4; and

FIG. 6 is a perspective view of a blade incorporating another means of achieving an improved stiffness distribution according to my invention; and

FIG. 7 is a perspective view of a blade incorporating still another means of achieving an improved stiffness distribution according to my' invention; and

' FIG. 8 is a graph illustrating the effect of the desired change in the stiffness distribution on the fundamental torsional frequency and on the fundamental flexural frequency in a blade constructed according to my invention.

Referring now more particularly to the drawings, indicated diagrammatically in FIGS. la and lb is a typical iluid-ilow machinery blade. Consider the blade shown as being an elastic system, i.e., a cantilevered beam attached at the root and free at the tip, as indicated in y As such, it will have a number of fundamental FIG. la. natural frequencies at which it will vibrate. These frequencies include a fundamental natural torsional xfrequency and a fundamental natural flexural frequency. Yibration or bending in the flexural mode of vibration- 1s indicated by the dotted lines in FIG. la, and vibration or twisting inthe torsional mode is indicated by the dotted lines in FIG. 1b. If such a beam or blade is, for

example, made uniformly thicker along its length, the

ness affects both the torsional and the llexural modes of vibration by reason of higher resistance to motion. The relative tlexiblcness of an automobile leaf spring as compared to that of the slat of a Venetian blind is a common example of the relationship of thickness to stiffness. As stated above, in many types of turbomachinery, particularly in the first few stages of a compressor, the fundamental flexural frequency of the blade must be kept relatively low to avoid a known source of excitation, such as an external vibrating impulse. An undesired excitation source may be present, for example, as a result 0f asymmetric conditions existing in the inlet area of the compressor, such as two high pressure areas located 180 apart. As stated above, it had been thought impossible, particularly in the first few stages of a compressor wherein elongated flexible blades are used, to raise the torsional frequency by making the blades thicker or stiffer lengthwise without causing a correspondingly undesirable change in the first llexural frequency. The problem could also arise in the latter stages of the compressor' downstream of the inlet, where short blades are utilized, if a known excitation source or impulse would require shifting of the response frequency of the blade to avoid coincidence with the impulse frequency, although the problem in this latter case is of a less serious nature.

To better show how the above-described asymmetric condition is related to compressor rotor r.p.m., reference may be had to FIG. 2 which is a frequency plot of the sort useful in designing typical fluid-flow machinery blades. Plotted in the drawing are the frequencies of a number of excitation sources, in addition to the one described, and the llexural vibration frequency of a typical compressor blade during operation of the compressor. ln the given example wherein the asymmetric condition is in the form of the two high pressure areas, the excitation source is plotted as a solid line running at an angle upwards from left to right in the diagram. This plot being related to rotor r.p.m. may be referred to as the two per rev line, i.e., a rotor blade will be affected twice during one revolution. In the diagram the two per rev line is intersected by a dot-dash line representing a preferred level of the first flexural frequency, and by a dot-dot-dash line indicative of a lirst llexural frequency which is undesirable. Note that the `flexural frequency rises with a rise in operating speed because of the effect of centrifugal force, among other things, which tends to stiffen the blade. Where the two per rev line intersects the flexural frequency line resonance occurs and the result is unwanted vibration. Accordingly, it is necessary to avoid coincidence of the first flexural frequency and the two per rev line within the operating range of the compressor. This holds true, of course, whether the excitation occurs only once or even four or more times per revolution. It might seem to be obvious from FIG. 2 that the first flexural frequency could be raised, incident to raising the torsional frequency, in a manner which would avoid an undesirable coincidence with a known source of excitation. However, in the typically long flexible blade utilized in the compressor inlet area this is very difficult to do because of the blades increased susceptibility to a plurality of modes of vibration. If it were to be done by increasing the size of the blade, the added weight and/or chord width which would result in an unharmful increase in the first flexural frequency would, in most instances, be undesirable. ln any event, in advanced airborne turbomachinery applications such an increase in weight or size of the blade would be prohibitive.

l have discovered that it is possible to significantly reduce susceptibility to flutter by increasing the torsional frequency of the blade without, at the same time, substantially affecting either the size or weight of the blade or requiring that there be an unwanted change in the first flexural frequency. I have done this by adjusting the strength or stiffness distribution along a certain selected portion of the blade length. To understand how my improved stiffness distribution effects the desired change in the torsional frequency, it must be realized that the frequencies at which a fluid-flow machinery blade will vibrate are dependent primarily on certain of its geometrical properties, i.e., its mass and stiffness. The effect of these parameters on frequency is most pronounced in the airfoil portion of the blade. The thickness distribution over the length of the airfoil will affect its stiffness distribution and to a lesser extent its mass distribution, the latter being a result of the fact that the mass distribution varies approximately linearly with the thickness distribution whereas the stiffness distribution varies approximately as the cube of the thickness distribution. The thickness distribution, therefore, influences the frequencies at which the blade vibrates by its elfe-:t on stiffness, and on mass.

Stilfness, on the other hand, is most pronounced in its effect on frequency at the local position of the blade span of the greatest flexural and torsional moments. Moment ca u be expressed algebraically as F XD, where F :force (load) and D=distance. A bending moment is set up when an external force or load is imposed on a cantilevered beam, such as that shown in FIG. la to deflect the beam. The moment occurs across the length of the bend curvature caused by the beam flexing. Flexing of the beam, in this case a blade, causes fthe blade bers on the convex side to lengthen under tensile stresses, and the fibers on the concave side to shorten under compressive stresses, thus the blade is distorted. Twisting or torsional moment, on the other hand, can be expressed algebraically for a round shaft as P p, where P=the resultant of the twisting forces (load and p=distance of the resultant force from the axis of the beam. Although torsional moment for a noncircular beam is actually more complex, in any case where twisting occurs, the outermost bers are in tension and therefore distorted. By referring to FIGS. la and 3 it will be seen that the torsional moment, or torque, and the flexural moment is highest in the root portion of the blade, i.e., most of the twisting and bending takes place in this area. Since distortion tends to be greatest in the `root area which is the region of maximum flexural and torsional moments, additional stiffness in this region will resist the tendency to distort by stiiening the region. With increased stiffness vibration frequencies will rise because of the concomitant increased resistance to motion.

However, while the maximum moment or strain in flexure occurs in the root portion of the blade airfoil, FIG. 3 also shows that the flexural moment or strain decreases very rapidly proceeding from the root portion to the tip portion along the airfoil when the compressor is up to speed. It will further be apparent from the moment relationships shown in the curves of FIG. 3 that a change in stiffness distribution, effected primarily by a change in the thickness distribution outside the region of the root portion (and the tip portion), will have a substantial effect on the torsional frequency but will have relatively little effect on the first flexural frequency. In other words, while the one curve shows the aforementioned rapid decrease in flexural moment or strain, the other curve indicates that the torsional moment or strain of oscillation does not decrease rapidly in magnitude as a function of blade length, but remains considerable over approximately 80% of the blade length. In light of the aforementioned relationship of thickness to stiffness and the relationship, in turn, of stiffness to moment, both torsional and flexural, I have taken advantage of the factors shown diagrammatically in FIG. 3 to increase stiffness in the region of the blade wherein the average difference in the flexural and torsional moment is the largest. Although the change in stifnss at first would appear to be most effective where the percent difference between the two curves is largest, this approach must not be used indiscriminately since the 75 largest percent difference between the curves may actually exist near the root portion where an increase in stiifness could cause an undesirable change in the rst flexural frequency. Since the torsional moment or torque remains considerable over about 80% of the airfoil when the compressor is running at its normal operating speed, land since I have shown it to be undesirable to increase stiffness in the area of the first 25% of the blade length due to the effect on the iirst iiexural frequency, I have concluded that the stiffness should be upwardly adjusted over an intermediate portion of the blade, say, the portion from approximately 1A to @A of overall blade length.

In FIG. 4 there is shown atypical solid cast or forged turbomachinery blade having a base 2 and an airfoil 4 including a root portion 4a, a tip portion 4b and an intermediate portion 4c. In this embodiment of my invention the stiffness distribution in the intermediate portion 4c is improved by reason of a particular adjustment in the thickness distribution thereof in keeping with the principles discussed above. Specifically, in this embodiment of my improved or high-torsion blade, as is shown in FIG. 5, the blade in constructed so rthat whereas the thickness-tochord ratio (tm/c) over approximately the first l25% of the blade is decreasing at a decreasing rate, thereafter, i.e., after the point of inflection in a plot of the curve of the slope of the line in FIG. 5, the tm/c is decreasing at an increasing rate. In other words, the thickness (or stiffness) distribution in the airfoil decreases rapidly in the general area of the Iroot portion, remains fairly constant over substantially the greater part of the intermediate portion, and, thereafter, again decreases rapidly on out through the tip portion. 'I'he adjustment in the thickness distribution therefore covers approximatelyv 60 to 80% of the overall length of the blade.

Another way to increase torsional frequency by achieving the desired stiffness distribution described above is to fabricate a portion of the blade hollow such as is shown in FIG. 6. In a hollow blade the desired effect is achieved by a wall or skin thickness distribution similar to the total thickness distribution of the solid blade shown in FIG. 3. A further way of accomplishing the desired stiffness distribution is to manufacture a blade, of perhaps arbitrary thickness distribution, of heterogeneous material or materials having a variable modulus of elasticity for torsional resistance rigidity wherein E (modulus elasticity) M (bending moment) XP (radius of curvature) I (moment of inertia) In this case, the blade is designed so lthat the root portion has an accentuated bending stiffness, for example, by means of a particular orientation of the crystal structure or the fibers of the blade material, and the intermediate portion has a different crystalline or fibrous orientation to achieve an accentuation of torsional stilness, as is shown schematically in FIG. 7. It is also possible to vary the stiffness distribution along the chord from leading to trailing edges, in the Ways discussed above; however, the resulting increase in torsional frequency will not be as great.

The graph in FIG. 8 showsthat I can provide a blade that Will have increased resistance to vibrational instability in the form of flutter by reason of an increase in torsional frequency provided by a predetermined change in stiffness distribution, which change, however, will not substantially affect the rst flexural frequency. The exact change in the stiifness distribution will depend, of course, on the particular application for which the blade is proposed, i.e., on the nature of the machinery, the number and type of excitation sources, and/or the extent of the increase in torsional frequency desired. In lany case, however, the stiifness distribution in my so-called hightorsion blade will vary from root to tip substantially in the manner as stated above.

In summary, compared to a conventional fluid-flow machinery blade, my improved blade is more stable and l6 less likely to be subject totlutter or vibrational instability due Ito its having been provided with a higher fundamental torsional frequency without the accompanying undesirable rise in the fundamental flexural frequencypreviously 4through to be inescapable.

What I therefore desire to cl-aim by Letters Patent is: l. 4An axial flow compressor or turbine blade adapted to -be mounted on a rotor located in a casing having an inlet at one end and an outlet at the other end, said blade comprising a solid airfoil section including root, tip and intermediate portions, said airfoil section having an improved stitfness distribution wherein the thickness distribution in the airfoil section, proceeding from the endfVVV of the root portion remote to the tip portion, initially decreases at a decreasing rate and thereafter decreases at an increasing rate, the blade having a relatively-high fundamental torsional frequency `without a correspondingly high fundamental flexural frequency.

2. A fluid-flow machinery blade having a solid airfoil section including root, tip, and intermediate portions wherein the stiffness distribution in said airfoil section is determined by an accentuated bending stilness in the root portion thereof by reason of a predetermined iixed ilexure-responsive arrangement of blade material iibers, said airfoil section also having an accentuated torsional stiffness in the intermediate portion thereof by reason of a predetermined fixed torque-responsive arrangement of said material fibers whereby the blade has a relatively high fundamental torsional frequency wit-hout a correspondingly high fundamental flexural frequency.

3. A Huid-flow machinery blade having a solid airfoil section including root, tip, and intermediate portions wherein the stiffness distribution in said airfoil section is determined by an accentuated bending stilfness in said root portion by reason of a predetermined fixed ilexureresponsive arrangement of the crystalline structure of d high fundamental flexural frequency.

4. An axial tlow compressor or turbine -blade adapted to be mounted on a rotor located in a casing having an inlet at one end and an outlet at the other end, said blade comprising a solid `airfoil section including root, tip, and intermediate portions, said airfoil section having a stiffness distribution which is -determined by a thickness, distribution in said airfoil such that a curve of the slope of the thickness-to-chord ratio has a single point of inflection between the root portion and the tip portiomthe slope of the thickness-to-chord ratio from the end of the root portion remote from the tip portion decreasing at a decreasing rate to said point of inflection, said slope thereafter decreasing at an increasing rate to said tip lover the length of the blade airfoil section, starting at the end of the root portion remote from the tip portion and proceeding to the tip portion, has a single point of iniiection located at approximately 25% of the airfoil section length, the slope in the root portion decreasing at a decreasing rate to said point of inflection, the slope thereafter decreasing at an increasing rate.

6. An axial ow compressor or turbine blade adapted to be mounted on a rotor located in a casing having an inlet at one end and an outlet at the other end, said blade comprising a solid airfoil section including root, tip, and

intermediate portions, said airfoil section having a stiffness distribution which is determined by a thickness distribution such that vthe thickness-to-chord ratio, starting at the end of the root portion remote from the tip portion and proceeding to the tip portion of the airfoil section, decreases at a decreasing rate over approximately the first 25% of the airfoil section and thereafter decreases at an increasing rate for approximately the next 50% ofthe airfoil section.

References Cited in the 61e of this patent UNITED STATES PATENTS 1,041,269 Guyer Oct. 15, 1912 8 Schellens Apr. 18, Baumann Sept. 21, Stuart Apr. 21, Smith Aug. 9, Zagorski et al. Mar. 7, Martens et a1 Mar. 6, McCauley May 26, lDe Mey et a1. Oct. 26, H1111 Nov, 24, Klint Dec. 8,

FOREIGN PATENTS Great Britain Apr. 8, Germany Apr. 12, 

